If `f^(prime)(x)=|x|-{x},` where {x} denotes the fractional part of `x ,` then `f(x)` is decreasing in `(-1/2,0)` (b) `(-1/2,2)` `(-1/2,2)` (d) `(1/2,oo)`

lim_(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part of x) is equal to

lim_(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional part of x is equal to

The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fractional part in [-1,1] is (a) [-1,1]-(1/(2,1)) (b) [-1,-1/2]uu[(0,1)/2]uu{1} (c) [-1,1/2] (d) [-1/2,1]

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

The period of function 2^({x})+sinpix+3^({x/2})+cos2pix (where {x} denotes the fractional part of (x) is 2 (b) 1 (c) 3 (d) none of these

Let f(x)=inte^x(x-1)(x-2)dxdot Then f decreases in the interval (a) (-oo,-2) (b) -2,-1) (c) (1,2) (d) (2,+oo)

If f(x)={{:(sqrt({x}),"for",xcancelinZ),(1,"for",x in Z):} and g(x)={x}^(2) where {.} denotes fractional part of x then area bounded by f(x) and g(x) for x in 0,6 is

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)

Discuss the continuity of f(x)={x{x}+1,0lt=x<1 and 2-{x},1lt=x<2 where {x} denotes the fractional part function.